The invention is directed to a venting device for the fuel tank of a motor vehicle. A known venting device is disclosed in DE-C 33 46 103. Absorption of the fuel in the fuel vapor filter, which normally consists of activated charcoal, is an exothermic process. It is therefore desirable that the coldest possible air be supplied to the filter for aeration. Consequently, the aeration line generally is laid so that it opens into the atmosphere outside the warm engine compartment, near the underside of the vehicle, so that relatively cool air is thus suctioned through the filter. However, this position of the outlet of the aeration line can entail problems. For instance, the outlet can be temporarily plugged by freezing liquid. In this case, the fuel vapor filter can implode due to action of the vacuum from the intake system of the internal combustion engine in the venting system.